Blind SNR estimation

ABSTRACT

A method for estimating the signal to noise ratio (=SNR) of a modulated communication signal including a data symbol component and a noise component is characterized in that an intermediate SNR value of the modulated communication signal is derived from a data assisted maximum-likelihood estimation, the assisting data not being known in advance but being reconstructed from samples of the modulated communication signal, and that an estimated SNR value is determined by a controlled non-linear conversion of the intermediate SNR value. This method allows an SNR estimation with high accuracy even for low numbers of processed samples.

BACKGROUND OF THE INVENTION

The invention is based on a priority application EP 04293155.0 which ishereby incorporated by reference.

The invention relates to a method for estimating the signal to noiseratio (=SNR) (γ) of a modulated communication signal (r_(n)) including adata symbol component (s_(n)) and a noise component (n_(n)).

An overview of SNR estimation techniques is given in D. R. Pauluzzi, N.C. Beaulieu, IEEE Trans. Comm. Vol. 48, Nr. 10, P. 1681-1691 (October2000).

In order to provide optimal functioning of advanced mobile radiomodules, accurate signal to noise ratio (=SNR) estimation of modulatedcommunication signals is necessary. On the physical layer, SNR valuesare used in maximum-ratio combining and turbo-decoding. On higherlayers, SNR values are used for call setup, macro diversity and handovercontrol.

In environments with varying SNR, such as mobile radio networks, thedetermination of an SNR value must be rather quick.

The SNR value γ is defined as the ratio of signal power and noise power,i.e.$\gamma = {\frac{{signal}\quad{power}}{{noise}\quad{power}} = {\frac{{{{signal}\quad{amplitude}}}^{2}}{{noise}\quad{power}}.}}$SNR estimation can be done data-assisted (=DA) or Non-data assisted(NDA). The latter is often called a “blind” estimation.

In the case of data assisted SNR estimation, a set of samples (with onesample typically corresponding to one bit) is known in advance. After atransmission of the set of samples, the received data is compared withthe original data by means of a data-assisted maximum likelihoodestimation. The known set of samples can be a preamble or a trainingsequence.

If the transmitted set of samples is not known in advance, a blindestimation algorithm must be applied. Known algorithms of blind SNRestimation include

-   -   a) standard received data aided (=RDA) maximum likelihood SNR        estimation (see e.g. D. Pauluzzi, N. Beaulieu, IEEE Trans.        Comm., Vol 48, No 10, pp. 1681-1691, October 2000),    -   b) iterative SNR estimation (see e.g. B. Li et al., IEEE Commun.        Lett. Vol 6, No 11, pp. 469-471, November 2002), and    -   c) Kurtosis SNR estimation (see e.g. R. Matzner, K. Letsch,        Proc. IEEE-IMS Workshop on Information Theory and Statistics,        Alexandria/Va., USA, p. 68ff, October 1994).

However, these known algorithms are rather inaccurate for low numbers ofsamples. Moreover, in particular the iterative SNR estimation iscumbersome and time consuming.

SUMMARY OF THE INVENTION

It is the object of the present invention to provide a robust SNRestimation method for a modulated communication signal, wherein themethod has a high accuracy even for low numbers of processed samples.

This object is achieved by a method as introduced in the beginning,characterized in that an intermediate SNR value ({circumflex over(γ)}_(RDA)) of the modulated communication signal is derived from a dataassisted maximum-likelihood estimation, the assisting data not beingknown in advance but being reconstructed from samples of the modulatedcommunication signal (r_(n)), and that an estimated SNR value({circumflex over (γ)}_(RDA-ER)) is determined by a controllednon-linear conversion of the intermediate SNR value ({circumflex over(γ)}_(RDA))

The inventive method estimates the SNR of the modulated communicationsignal by means of a conversion of the intermediate SNR value. Theintermediate SNR value is obtained by a standard RDA maximum likelihoodSNR estimation of the modulated communication signal. The intermediateSNR value {circumflex over (γ)}_(RDA) deviates from the true SNR valueγ. In particular, for small values of the true SNR value γ, i.e. γ→0,{circumflex over (γ)}_(RDA) is much larger than γ. This deviation iscompensated for by the controlled non-linear conversion of theintermediate SNR value.

The controlled non-linear conversion can be done by means of aconversion table based on an experimentally predetermined correlationbetween {circumflex over (γ)}_(RDA) and γ. It is preferred, however, tomodel the correlation between {circumflex over (γ)}_(RDA) and γmathematically and to use the modelled correlation for conversion. Formodelling, information about and/or suitable assumptions for thecharacteristics of the modulated communication signal are useful. Inparticular, the type of modulation should be known. It has been foundthat signals modulated by binary phase shift keying (=BPSK) can behandled very well by the inventive method. Moreover, the type of noisein the modulated communication signal can often be assumed to have aGaussian distribution.

With the aid of the highly accurate and robust estimated SNR valuesobtained over a broad SNR range, as determined by means of theinvention, it is possible to improve receiver performance, which in turnallows for distressing of margins e.g. in network planning, inparticular lower UL/DL transmission power requirements and largerdistances between base stations, nodes B and the like.

A highly preferred variant of the inventive method is characterized inthat the controlled non-linear conversion is performed by a correctionfunction Ψ⁻¹, with {circumflex over (γ)}_(RDA-ER)=Ψ⁻¹({circumflex over(γ)}_(RDA)), wherein the correction function Ψ⁻¹ is the inverse functionof an estimated deviation function Ψ, with the estimated deviationfunction Ψ approximating a true deviation function Ψ_(true) correlatingthe deviation of {circumflex over (γ)}_(RDA) from γ, i.e. {circumflexover (γ)}_(RDA)=Ψ_(true)(γ) and Ψ(γ)≈Ψ_(true)(γ). Typically, theestimated deviation function is determined by a mathematic model. Itsinverse function, i.e. the correction function, can be obtained bymirroring the estimated deviation function at the bisecting line of thefirst quadrant in the coordinate system. If the estimated deviationfunction is simple enough, its inverse function can also be calculatedanalytically. The estimated deviation function Ψ(γ) can be calculated bysetting it equal to the intermediate SNR signal, which in turn is theratio of the estimated signal power and the estimated noise power of themodulated communication signal. The estimated signal power and estimatednoise power, then, must be expressed as a function of γ, with the latterrequiring suitable assumptions, such as e.g. an infinite number ofsamples to be processed.

In a preferred further development of this method, Ψ is chosen such thatΨ(γ)=Ψ_(true)(γ) for large numbers of N, i.e. N→∞, with N being thenumber of samples of the modulated communication signal (r_(n)) beingprocessed. The estimated deviation function found in this way is thenapplied to data with a finite number of samples, too. In many cases, inparticular with a BPSK modulation and Gaussian noise distribution,Ψ_(true)(γ) can be determined accurately for N→∞. The latter assumptionis justified in most real situations, when sufficiently large numbers ofsamples are available. In particular, a number of 100 samples or more issufficient.

In a further preferred development of said variant of the inventivemethod,${\Psi(\gamma)} = {\frac{1}{\frac{\gamma + 1}{\left( {{\sqrt{\gamma}{{erf}\left( \sqrt{\frac{\gamma}{2}} \right)}} + \sqrt{\frac{2}{\pi}{\mathbb{e}}^{- \frac{\gamma}{2}}}} \right)^{2}} - 1}.}$This choice of Ψ(γ) gives highly accurate results in case of a BPSKmodulation of the modulated communication signal.

In an advantageous development of the variant, Ψ⁻¹ is applied by meansof an approximation table. An approximation table provides very quickaccess to values of the correction function, which are listed in thetable. Alternatively, online numerical or analytical calculation ofvalues of the correction function is also possible, but more timeconsuming.

Further preferred is a development of said variant wherein${\Psi(\gamma)} = {{\Psi_{HA}(\gamma)} = {\sqrt{\gamma^{2} + \left( \frac{2}{\pi - 2} \right)^{2}}.}}$This hyperbolic function is a good approximation of Ψ_(true)(γ) in caseof BPSK modulation. Its inverse can be calculated straightforwardly as${{\Psi_{HA}^{- 1}(\gamma)} = {{\sqrt{{\gamma^{2}\left( \frac{2}{\pi - 2} \right)}^{2}}\quad{for}\quad\gamma} \geq \frac{2}{\pi - 2}}},{and}$${\Psi_{HA}^{- 1}(\gamma)} = {{0\quad{for}\quad\gamma} = {\leq {\frac{2}{\pi - 2}.}}}$Thus, the correction function is available analytically, whichsimplifies and accelerates the determination of the estimated SNR value{circumflex over (γ)}_(RDA-ER).

In another variant of the inventive method, the number N of samples ofthe modulated communication signal (r_(n)) being processed is equal orless than 500, preferably equal or less than 100. In these cases, theinventive method already provides estimated SNR values of high accuracy,whereas known methods show worse accuracy. For higher values of N, suchas an N of 1000 or larger, it is worth mentioning that the inventivemethod provides equally accurate estimated SNR values as known methods,but typically with less effort.

Also in the scope of the invention is a computer program for estimatingthe signal to noise ratio (γ) of a modulated communication signal(r_(n)) according to the inventive method. The computer program may besaved on a storage medium, in particular a hard disk or a portablestorage medium such as a compact disc.

The invention also comprises a receiver system for estimating the signalto noise ratio (γ) of a modulated communication signal (r_(n)) accordingto the inventive method. The receiver system comprises a receiver unit.The receiver unit can receive transmitted signals, with the transmissioncarried out by radio or an optical fibre line, e.g.. The inventivemethod can be performed directly with the received transmitted signals,i.e. at the receiver unit. Alternatively, the inventive method can beapplied after a channel decoding, such as turbo decoding, of thereceived transmitted signals. In the latter case, the method isperformed with “soft” signals.

Finally, the invention is also realized in an apparatus, in particular abase station or a mobile station, comprising an inventive computerprogram and/or an inventive receiver system as described above. Atypical mobile station is a mobile phone. An inventive apparatus can bepart of a 3G or B3G network, in particular a UMTS network or a WLANnetwork.

Further advantages can be extracted from the description and theenclosed drawing. The features mentioned above and below can be used inaccordance with the invention either individually or collectively in anycombination. The embodiments mentioned are not to be understood asexhaustive enumeration but rather have exemplary character for thedescription of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention is shown in the drawing.

FIG. 1 shows a binary transmission system with a noisy channel for usewith the inventive method;

FIG. 2 shows plots of an estimated deviation function Ψ(γ) for a BPSKreal channel and a hyperbolic function Ψ_(HA)(γ) which approximates theformer function, as well as their inverse functions in accordance withthe invention;

FIG. 3 a shows a diagram plotting normalized mean square errors ofestimated SNR values with respect to the true SNR values as a functionof the true SNR value, for standard RDA maximum likelihood SNRestimation (state of the art), inventive RDA-ER and inventive RDA-ERHA,with 100 samples processed per SNR estimation;

FIG. 3 b shows a diagram corresponding to FIG. 3 a, with 1000 samplesper SNR estimation;

FIG. 4 a shows a diagram plotting normalized mean square errors ofestimated SNR values with respect to the true SNR values as a functionof the true SNR value, for standard RDA maximum-likelihood SNRestimation (state of the art), inventive RDA-ER, Iterative method (stateof the art) and Kurtosis method (state of the art) with 100 samplesprocessed per SNR estimation;

FIG. 4 b show a diagram corresponding to FIG. 4 a, with 1000 samplesprocessed per SNR estimation.

DETAILED DESCRIPTION OF THE DRAWINGS

The invention deals with the estimation of SNR values in a transmissionsystem, such as a radio telephone network. A transmission system for usewith the invention is shown schematically in FIG. 1. At a source S,binary data is generated. The binary data may contain information of atelephone call, for example. The binary data consists of a number ofbits b_(n), with n: the index number of the bits, running from 0 to N−1,with N: the total number of bits of the binary data. Each bit may have avalue of 0 or 1. In order to transport the binary data, it is modulatedin a modulator M. A typical modulation is the binary phase shift keying(BPSK) modulation, resulting in values of a data symbol component s_(n)of +1 or −1. At the physical transmission of the data symbol components_(n), typically applying a carrier frequency, s_(n) is amplified by afactor α. Also, noise n_(n) is superposed by the channel to theamplified data symbol component α·s_(n). The amplification factor α andthe noise level are unknown initially. Thus in total, a modulatedcommunication signal r_(n)=α·s_(n)+n_(n) is generated and ready fordetection at a receiver system. The receiver system may be part ofamobile phone, for example. During the physical transport, other datasymbol components may be transmitted at the same time at other frequencyranges and/or at other (spreading) code ranges. These other data symbolcomponents can be neglected in this context; they may affect the noisecomponent n_(n), though.

In the following, a BPSK modulation is assumed as well as a realchannel, with a noise probability density function (=PDF) of Gaussiantype${{p\left( n_{n} \right)} = {\frac{1}{\sigma\sqrt{2\pi}}{\mathbb{e}}^{- \frac{n_{n}^{2}}{2\sigma^{2}}}}},$with σ: standard deviation or noise amplitude. However, other signalcharacteristics are possible in accordance with the inverntion.

When making a data-aided (DA) maximum-likelihood SNR estimation, anestimated amplitude {circumflex over (α)} with known “pilots” s_(n),i.e. a set of N known data symbol component values, is calculated as${\hat{\alpha} = {{E\left\{ \frac{r_{n}}{s_{n}} \right\}} = {{\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}\frac{r_{n}}{s_{n}}}} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{r_{n}s_{n}}}}}}},$with s_(n)={+1, −1}. Note that a hat ˆ above a value indicates anestimated value, and E is the estimation operation determining the meanvalue of its input values. The estimated noise power {circumflex over(σ)}² (second moment) is calculated as $\begin{matrix}{{\hat{\sigma}}^{2} = {E\left\{ \left( {r_{n} - {\hat{\alpha}\quad s_{n}}} \right)^{2} \right\}}} \\{= {{E\left\{ r_{n}^{2} \right\}} - {{\hat{\alpha}}^{2}E\left\{ s_{n}^{2} \right\}}}} \\{{= {\frac{1}{N - v}{\sum\limits_{n = 0}^{N - 1}\left( {r_{n} - {\hat{\alpha}\quad s_{n}}} \right)^{2}}}},}\end{matrix}$with ν being a constant to be chosen according to literature (D. R.Pauluzzi, N. C. Beaulieu, I.c.) as follows: Maximum likelihood for σ²estimation: v=0; Bias elimination for σ² estimation: v=1; Minimum MSEfor σ² estimation: v=−1; Bias elimination for γ estimation: v=3; MinimumMSE for γ estimation: v=5. The data-aided SNR estimation then results in$\begin{matrix}{{\hat{\gamma}}_{DA} = \frac{{\hat{\alpha}}^{2}}{{\hat{\sigma}}^{2}}} \\{= \frac{\left( {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{r_{n}s_{n}}}} \right)^{2}}{{\frac{1}{N - v}{\sum\limits_{n = 0}^{N - 1}r_{n}^{2}}} - {\frac{1}{N\left( {N - v} \right)}\left( {\sum\limits_{n = 0}^{N - 1}{r_{n}s_{n}}} \right)^{2}}}} \\{= {\frac{\left( {N - v} \right)}{N}{{\hat{\gamma}}_{v = 0}.}}}\end{matrix}$

In case of a “blind”, i.e. received-data-aided (RDA) maximum likelihoodSNR estimation, the “pilots” are estimated based on receiver decisions,identical to the first absolute moment. The estimated amplificationfactor {circumflex over (α)} is calculated as$\hat{\alpha} = {{E\left\{ {r_{n}{\hat{s}}_{n}} \right\}} = {{E\left\{ {r_{n}{{signum}\left( r_{n} \right)}} \right\}} = {{E\left\{ {r_{n}} \right\}} = {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{{r_{n}}.}}}}}}$

Noise power is estimated correspondingly (compare DA above).Accordingly, an SNR value is estimated, with${\hat{\gamma}}_{{{BPSK}\quad 1},{RDA}} = {\frac{\left( {\frac{1}{N}{\sum\limits_{n = 0}^{N - 1}{r_{n}}}} \right)^{2}}{{\frac{1}{N - v}{\sum\limits_{n = 0}^{N - 1}r_{n}^{2}}} - {\frac{1}{N\left( {N - v} \right)}\left( {\sum\limits_{n = 0}^{N - 1}{r_{n}}} \right)^{2}}}.}$

This value {circumflex over (γ)}_(BPSK1,RDA) is the result of thestandard RDA maximum likelihood SNR estimation, as known fromliterature.

However, by using estimated data symbol component values ŝ_(n) insteadof the true data symbol component values s_(n), error is introduced. Forsufficiently large SNR values γ, {circumflex over (γ)}_(BPSK1,RDA)approximates γ very well, but for small values of γ, the estimatedvalues {circumflex over (γ)}_(BPSK1,RDA) are too large.

According to the invention, the {circumflex over (γ)}_(BPSK1,RDA) valueis set equal to an estimated deviation function Ψ(γ). For this purpose,the terms of {circumflex over (γ)}_(BPSK1,RDA) are expressed asfunctions of the true SNR value γ, requiring some approximations andassumptions:$\hat{\alpha} = {{E\left\{ {r_{n}} \right\}} = {{E\left\{ {\alpha + {n_{n}}} \right\}} = {{\frac{1}{\sigma}\sqrt{\frac{2}{\pi}}{\int_{0}^{\infty}{\rho\quad{\mathbb{e}}^{\frac{\rho^{2} + \alpha^{2}}{2\quad\sigma^{2}}}\quad\cos\quad{h\left( {\frac{\alpha}{\sigma^{2}}\rho} \right)}{\mathbb{d}\rho}}}} = {{{{\alpha erf}\left( \sqrt{\frac{\gamma}{2}} \right)} + {\sigma\sqrt{\frac{2}{\pi}}{\mathbb{e}}^{\frac{\gamma}{2}}{\hat{\alpha}}^{2}} + {\hat{\sigma}}^{2}} = {{E\left\{ r_{n}^{2} \right\}} = {{\frac{1}{\sigma\sqrt{2\quad\pi}}{\int_{0}^{\infty}{\sqrt{\upsilon}{\mathbb{e}}^{\frac{\upsilon + \alpha^{2}}{2\sigma^{2}}}\cos\quad{h\left( {\frac{\alpha}{\sigma^{2}}\sqrt{\upsilon}} \right)}\quad{\mathbb{d}\upsilon}}}} = {{\alpha^{2} + {\sigma^{2}{\hat{\gamma}}_{{{BPSK}\quad 1},{RDA}}}} = {\frac{{\hat{\alpha}}^{2}}{{\hat{\sigma}}^{2}} = {\frac{\left( {E\left\{ {r_{n}} \right\}} \right)^{2}}{{E\left\{ r_{n}^{2} \right\}} - \left( {E\left\{ {r_{n}} \right\}} \right)^{2}} = {\frac{1}{\frac{E\left\{ r_{n}^{2} \right\}}{\left( {E\left\{ {r_{n}} \right\}} \right)^{2}} - 1} = {\frac{1}{\frac{\gamma + 1}{\left( {{\sqrt{\gamma}{{erf}\left( \sqrt{\frac{\gamma}{2}} \right)}} + {\sqrt{\frac{2}{\pi}}{\mathbb{e}}^{\frac{\gamma}{2}}}} \right)^{2}} - 1}\overset{\bigtriangleup}{=}{\Psi(\gamma)}}}}}}}}}}}}$

In particular, the one-dimensional Gaussian type noise PDF as defined inthe beginning has been introduced in this calculation, and it is basedon the BPSK modulation (indicated by the index BPSK1, where the “1”represents the one-dimensionality of the real channel and its noise).

The result {circumflex over (γ)}_(BPSK1,RDA) of the standard RDA maximumlikelihood estimation is used as a starting point for the actualcalculation of an estimated SNR value {circumflex over(γ)}_(BPSK1,RDA-ER) in accordance with the invention. For this reason,the {circumflex over (γ)}_(BPSK1,RDA) is called an intermediate SNRvalue. The “ER” index of {circumflex over (γ)}_(BPSK1,RDA-ER) indicatesan extended range, i.e. an improved range of application with theinvention. For calculating {circumflex over (γ)}_(BPSK1,RDA-ER), theinverse function Ψ⁻¹ of the estimated deviation function Ψ(γ) isdetermined, and the intermediate SNR value {circumflex over(γ)}_(BPSK1,RDA) is assigned to Ψ⁻¹, with {circumflex over(γ)}_(BPSK1,RDA-ER)=Ψ⁻¹({circumflex over (γ)}_(BPSK1,RDA)). Note that${\Psi^{- 1}(x)} = {{0{\quad\quad}{for}\quad x} \leq {\frac{2}{\pi - 2}.}}$The correlation of {circumflex over (γ)}_(BPSK1,RDA)=Ψ(γ) is, due to theassumptions and simplifications necessary to express {circumflex over(γ)}_(BPSK1,RDA) in terms of γ, only an approximation of the true andexact correlation {circumflex over (γ)}_(BPSK1,RDA)=Ψ_(true)(γ). Thebetter Ψ(γ) approximates Ψ_(true)(γ), the more accurate is the estimatedSNR value {circumflex over (γ)}_(BPSK1,RDA-ER) in accordance with theinvention.

In the above-calculated case of BPSK over a real channel, the estimateddeviation function Ψ cannot be inverted to a closed form inversefunction, so numerical calculation is necessary. However, forsimplification, the estimated deviation function Ψ can be approximatedby a hyperbolic function Ψ_(HA) which is easy to invert: $\begin{matrix}{{{\Psi(x)} \approx {\Psi_{HA}(x)}} = \sqrt{x^{2} + \left( \frac{2}{\pi - 2} \right)^{2}}} & \quad \\{{{\Psi^{- 1}(x)} \approx {\Psi_{HA}^{- 1}(x)}} = \sqrt{x^{2} - \left( \frac{2}{\pi - 2} \right)^{2}}} & {{\quad\quad}{{{for}{\quad\quad}x} \geq \frac{2}{\pi - 2}}} \\{{\Psi^{- 1}(x)} = {{\Psi_{HA}^{- 1}(x)} = 0}} & {{{for}\quad x} \leq {\frac{2}{\pi - 2}.}}\end{matrix}$Then the inventive estimated SNR value can be calculated as{circumflex over (γ)}_(BPSK1,RDA−ERHA)=Ψ_(HA) ⁻¹({circumflex over(γ)}_(BPSK1,RDA)).

In FIG. 2, the function${\Psi(\gamma)} = \frac{1}{\frac{\gamma + 1}{\left( {{\sqrt{\gamma}{{erf}\left( \sqrt{\frac{\gamma}{2}} \right)}} + {\sqrt{\frac{2}{\pi}}{\mathbb{e}}^{- \frac{\gamma}{2}}}} \right)^{2}} - 1}$as well as the function${\Psi_{HA}(\gamma)} = \sqrt{\gamma^{2} + \left( \frac{2}{\pi - 2} \right)^{2}}$which approximates the former function are plotted for comparison. Thedifferences are about 0.2 absolutely and about 10% relatively atmaximum. Their inverse functions, which are available by mirroring theplots at the bisecting line of the first quadrant (dashed line withoutsymbols), are also indicated in FIG. 2.

In order to quantify the accuracy of the inventive method for estimatingSNR values of modulated communication signals, different SNR estimationmethods of the state of the art and according to the invention have beentested.

A number N_(t) of tests is performed with every method. Each test isdone with a disjunctive set of N symbols (or bits, samples). Thecorresponding modulated communication signals r_(n) of each set, with nrunning from 0 to N−1, have a known true SNR value γ. In each test, anestimated SNR value {circumflex over (γ)}_(m) of the tested set isdetermined by means of the currently tested method, with m: test index(or index of tested sets) running from 0 to N_(t)−1. The distribution ofthe estimated SNR values {circumflex over (γ)}_(m) as compared with thetrue SNR value γ is analysed by calculating a normalized mean squareerror (NMSE) of {circumflex over (γ)}_(m):${{NMSE}\left\{ {\hat{\gamma}}_{m} \right\}} = {\frac{{MSE}\left\{ {\hat{\gamma}}_{m} \right\}}{\gamma^{2}} = {\frac{E\left\{ \left( {{\hat{\gamma}}_{m} - \gamma} \right)^{2} \right\}}{\gamma^{2}} = {\frac{1}{N_{t}\gamma^{2}}{\sum\limits_{m = 0}^{N_{t} - 1}{\left( {{\hat{\gamma}}_{m} - \gamma} \right)^{2}.}}}}}$

The NMSE values are, for each method, a function of the true SNR value γand a function of the number of samples N of each set.

Test results are plotted in FIG. 3 a. The abscissa shows the true SNR γin dB, and the ordinate shows on a logarithmic scale the NMSE values ofestimated SNR values for three different methods, i.e. standard RDAmaximum likelihood estimation of the state of the art, inventive RDA-ERmaximum likelihood estimation with the estimated deviation function Ψ asin FIG. 2, and inventive RDA-ERHA maximum likelihood estimation with theestimated deviation function Ψ_(HA) as in FIG. 2. For the diagram, allin all 10⁶ SNR estimations (tests) have been calculated, with N=100samples per SNR estimation.

For low SNR values (0 dB and less), the NMSE values of the inventiveRDA-ER and RDA-ERHA methods are much lower than the NMSE values of thestate of the art standard RDA method. In other words, the inventivemethods are more accurate in this range. In particular, at −10 dB and −5dB, the inventive methods are about 10 times more accurate than standardRDA. In said range, RDA-ER NMSE values are about half of the RDA-ERHANMSE values. For higher SNR values (5 dB and above), all three methodsare roughly equally accurate.

For FIG. 3 b, the same tests as for FIG. 3 a have been performed, butwith N=1000 samples per SNR estimation. The relative difference inaccuracy between state of the art RDA on the one hand and inventiveRDA-ER and RDA-ERHA is even higher, showing the improvement by theinventive method.

For FIG. 4 a, the same tests as for FIG. 3 a have been performed, withN=100 samples per SNR estimation again. The NMSE values of estimated SNRvalues are plotted for the standard RDA maximum likelihood estimationmethod of the state of the art, the inventive RDA-ER maximum likelihoodestimation method, the Iterative method of the state of the art, and theKurtosis method of the state of the art. The inventive RDA-ER method hasthe lowest NMSE values, indicating the highest accuracy, over a verybroad SNR range. In the range of 0 dB to 5 dB, the Iterative method isroughly equal to the inventive RDA-ER method.

For FIG. 4 b, the same tests as for FIG. 4 a have been performed, butwith N=1000 samples per SNR estimation. For low SNR values (0 dB andless), the inventive RDA-ER method, the Iterative method and theKurtosis method are equally accurate. For SNR values of 10 dB and above,the inventive RDA-ER method clearly outperforms the Iterative method.Moreover, the inventive RDA-ER method outperforms the Kurtosis methodbetween 0 dB and 15 dB.

In summary, the inventive SNR estimation method has been tested for aBPSK channel over a real AWGN channel. It outperforms or is at leastequal to known blind SNR estimation algorithms. The inventive method caneasily be used with other signal modulations over real or complexchannels. The inventive method requires only limited effort (a littlemore than the well-known maximum likelihood data assisted estimation);in particular, it does neither need iteration nor decoding/re-encodingof protected data. Finally, to avoid the storage and the handling of theoptimal interpolation curve Ψ⁻¹, a hyperbolical approximation isavailable which allows instantaneous computation with only minorperformance degradation.

1. Method for estimating the signal to noise ratio (=SNR) (γ) of amodulated communication signal (r_(n)) including a data symbol component(s_(n)) and a noise component (n_(n)), wherein an intermediate SNR value({circumflex over (γ)}_(RDA)) of the modulated communication signal isderived from a data assisted maximum-likelihood estimation, theassisting data not being known in advance but being reconstructed fromsamples of the modulated communication signal (r_(n)), and an estimatedSNR value ({circumflex over (γ)}_(RDA-ER)) is determined by a controllednon-linear conversion of the intermediate SNR value ({circumflex over(γ)}_(RDA)).
 2. Method according to claim 1, characterized in that thecontrolled non-linear conversion is performed by a correction functionΨ⁻¹, with {circumflex over (γ)}_(RDA-ER)=Ψ⁻¹({circumflex over(γ)}_(RDA)), wherein the correction function Ψ⁻¹ is the inverse functionof an estimated deviation function Ψ, with the estimated deviationfunction Ψ approximating a true deviation function Ψ_(true) correlatingthe deviation of {circumflex over (γ)}_(RDA) from γ, i.e. {circumflexover (γ)}_(RDA)=Ψ_(true)(γ) and Ψ(γ)≈Ψ_(true)(γ).
 3. Method according toclaim 2, characterized in that Ψ is chosen such that Ψ(γ)=Ψ_(true)(γ)for large numbers of N, i.e. N→∞, with N being the number of samples ofthe modulated communication signal (r_(n)) being processed.
 4. Methodaccording to claim 2, characterized in that${\Psi(\gamma)} = {\frac{1}{\frac{\gamma + 1}{\left( {{\sqrt{\gamma}{{erf}\left( \sqrt{\frac{\gamma}{2}} \right)}} + {\sqrt{\frac{2}{\pi}}{\mathbb{e}}^{- \frac{\gamma}{2}}}} \right)^{2}} - 1}.}$5. Method according to claim 2, characterized in that Ψ⁻¹ is applied bymeans of an approximation table.
 6. Method according to claim 2,characterized in that${\Psi(\gamma)} = {{\Psi_{HA}(\gamma)} = {\sqrt{\gamma^{2} + \left( \frac{2}{\pi - 2} \right)^{2}}.}}$7. Method according to claim 1, characterized in that the number N ofsamples of the modulated communication signal (r_(n)) being processed isequal or less than 500, preferably equal or less than
 100. 8. Computerprogram for estimating the signal to noise ratio (γ) of a modulatedcommunication signal (r_(n)) to noise ratio (=SNR) (γ) of a modulatedcommunication signal (r_(n)) including a data symbol component (s_(n))and a noise component (n_(n)), wherein an intermediate SNR value({circumflex over (γ)}_(RDA)) of the modulated communication signal isderived from a data assisted maximum-likelihood estimation, theassisting data not being known in advance but being reconstructed fromsamples of the modulated communication signal (r_(n)), and that anestimated SNR value ({circumflex over (γ)}_(RDA-ER)) is determined by acontrolled non-linear conversion of the intermediate SNR value({circumflex over (γ)}_(RDA)).
 9. Receiver system for estimating thesignal to noise ratio (γ) of a modulated communication signal (r_(n)) tonoise ratio (=SNR) (γ) of a modulated communication signal (r_(n))including a data symbol component (s_(n)) and a noise component (n_(n)),wherein an intermediate SNR value ({circumflex over (γ)}_(RDA)) of themodulated communication signal is derived from a data assistedmaximum-likelihood estimation, the assisting data not being known inadvance but being reconstructed from samples of the modulatedcommunication signal (r_(n)), and that an estimated SNR value({circumflex over (γ)}_(RDA-ER)) is determined by a controllednon-linear conversion of the intermediate SNR value ({circumflex over(γ)}_(RDA)).
 10. Apparatus, in particular a base station or a mobilestation, comprising a computer program for estimating the signal tonoise ratio (γ) of a modulated communication signal (r_(n)) to noiseratio (=SNR) (γ) of a modulated communication signal (r_(n)) including adata symbol component (s_(n)) and a noise component (n_(n)), wherein anintermediate SNR value ({circumflex over (γ)}_(RDA)) of the modulatedcommunication signal is derived from a data assisted maximum-likelihoodestimation, the assisting data not being known in advance but beingreconstructed from samples of the modulated communication signal(r_(n)), and that an estimated SNR value ({circumflex over(γ)}_(RDA-ER)) is determined by a controlled non-linear conversion ofthe intermediate SNR value ({circumflex over (γ)}_(RDA)).
 11. Apparatus,in particular a base station or a mobile station, comprising a receiversystem for estimating the signal to noise ratio (γ) of a modulatedcommunication signal (r_(n)) to noise ratio (=SNR) (γ) of a modulatedcommunication signal (r_(n)) including a data symbol component (s_(n))and a noise component (n_(n)), wherein an intermediate SNR value({circumflex over (γ)}_(RDA)) of the modulated communication signal isderived from a data assisted maximum-likelihood estimation, theassisting data not being known in advance but being reconstructed fromsamples of the modulated communication signal (r_(n)), and that anestimated SNR value ({circumflex over (γ)}_(RDA-ER)) is determined by acontrolled non-linear conversion of the intermediate SNR value({circumflex over (γ)}_(RDA)).